What is the definition of global mean sea level (GMSL) and its rate?

The term "sea level" has many meanings depending upon the context. In satellite altimetry, the measurements are made in a geocentric reference frame (relative to the center of the Earth). Tide gauges, on the other hand, measure sea level relative to the local land surface (see the tide gauge discussion and FAQ). The satellite altimeter estimate of interest is the distance between the sea surface illuminated by the radar altimeter and the center of the Earth (geocentric sea surface height or SSH). This distance is estimated by subtracting the measured distance between the satellite and sea surface (after correcting for many effects on the radar signal) from the very precise orbit of the satellite. At any location, the SSH changes over time due to many well understood factors (ocean tides, atmospheric pressure, glacial isostatic adjustment, etc.). By subtracting from the measured SSH an a priori mean sea surface (MSS), such as the CLS01 mean sea surface, and these known time-varying effects, we compute the sea surface height anomalies (SSHA). Each point in the global mean sea level (GMSL) time series plots is the area-weighted mean of all of
the sea surface height anomalies measured by the altimeter in a
single, 10-day satellite track repeat cycle (time for the satellite to begin repeating the same ground track). Our goal is to observe the changes of the GMSL due to less understood factors, such as ocean mass changes from melting land ice and groundwater depletion, thermal expansion and contraction of the oceans, and the interannual variability caused by phenomena such as the ENSO. Gaining more understanding of these different factors using other sources of information such as GRACE gravity measurements allows us to try to close the sea level budget and estimate the causes of GMSL changes (e.g., Leuliette & Miller, 2009 and Willis et al., 2008).

The term "global mean sea level" in the context of our research is defined as the area-weighted mean of all of
the sea surface height anomalies measured by the altimeter in a
single, 10-day satellite track repeat cycle. It can also be thought of as the "eustatic sea level." The eustatic sea level is not a physical sea level (since the sea levels relative to local land surfaces vary depending on land motion and other factors), but it represents the level if all of the water in the oceans were contained in a single basin. Changes to this eustatic level are caused by changes in total ocean water mass (e.g., ice sheet runoff), changes in the size of the ocean basin (e.g., GIA), or density changes of the water (e.g., thermal expansion). The time series of the GMSL estimates over the TOPEX and Jason missions beginning in 1992 to the present indicates a mostly linear trend after correction for inter-mission biases between instruments. The GMSL rate corrected for GIA represents changes in water mass and density in the oceans. These changes are thought to be predominantly driven by thermal expansion of the oceans and land ice melt (Greenland and Antarctic ice sheets and glaciers).